Denote by u(n) the largest principal specialization of the Schubert polynomial u(n) := max w∈S n S w (1, . . . , 1). Stanley conjectured that there is a limit lim n→∞ 1 n 2 log u(n), and asked for a limiting description of permutations achieving the maximum u(n). Merzon and Smirnov conjectured in [Eur. J. Math. 2 (2016), pp. 227-245] that this maximum is achieved on layered permutations. We resolve both of Stanley's problems restricted to layered permutations.